Similar articles

Abstract: To alleviate the wear of a thrust bearing in a reactor coolant pump (RCP) while ensuring the hydraulic performance of the pump, an adjoint-based optimization method is proposed in this study. This method reduces the axial force of the RCP impeller and synchronously improves the impeller’s hydraulic efficiency. By combining the adjoint solution with the radial basis function (RBF)-based mesh deformation, the optimization proceeds along the gradient direction, which greatly reduces the time and cost of the calculation. In the adjoint method, the adjoint equations in the rotating coordinate system are established, a joint objective function of the head constraint, hydraulic efficiency, and axial force is expressed, and then the blade surface sensitivity to the joint objective function is determined. In the RBF mesh deformation, the control points on the blade strand are evenly spaced, which ensures the smoothness of the deformed 3D twisted blade. Using the proposed optimization method, the hydraulic axial force of the impeller is reduced by approximately 3.8%, while the hydraulic efficiency of a scaled RCP impeller is increased by approximately 3.2%, and the head remains at an almost constant value. The obtained results validate the feasibility of the adjoint method for optimizing the design of centrifugal pumps.

This paper researches the blade shape optimization of pump for efficiency, axial force and head performances. The adjoint method is used to calculate the sensitivity.

基于伴随求解的核主泵轴向力优化方法

[1]Derakhshan S, Pourmahdavi M, Abdolahnejad E, et al., 2013. Numerical shape optimization of a centrifugal pump impeller using artificial bee colony algorithm. Computers & Fluids, 81:145-151.

[2]Dong W, Chu WL, 2015. Influence of balance hole diameter on performance and balance chamber pressure of centrifugal pump. Transactions of the Chinese Society for Agricultural Machinery, 46(6):73-77 (in Chinese).

[3]Du YY, Liu L, Liu G, et al., 2016. Study of axial force on impeller of mixed-flow pump by unsteady large eddy simulation. Fluid Machinery, 44(11):15-19 (in Chinese).

[4]Dwight RP, Brezillon J, 2006. Effect of approximations of the discrete adjoint on gradient-based optimization. AIAA Journal, 44(12):3022-3031.

[5]ESI-OpenCFD, 2007. OpenFOAM: the Open Source CFD Toolbox. OpenCFD Ltd, Bracknell, UK. https://www.openfoam.com/

[6]Gao H, Ga F, Zhao XC, et al., 2013. Analysis of reactor coolant pump transient performance in primary coolant system during start-up period. Annals of Nuclear Energy, 54(54):202-208.

[7]Gülich JF, 2014. Centrifugal Pumps, 3rd Edition. Springer, Berlin, Germany, p.495-505.

[8]Hsin CY, Chen KC, Tzeng YW, et al., 2010. Application of the adjoint method to the propeller designs. Journal of Hydrodynamics, 22(S1):484-489.

[9]Jameson A, 1988. Aerodynamic design via control theory. Journal of Scientific Computing, 3(3):233-260.

[10]Kong FY, Gao CL, Zhang XF, et al., 2009. Computation and experiment for axial force balance of canned motor pump PBN65-40-250. Transactions of the Chinese Society of Agricultural Engineering, 25(5):68-72 (in Chinese).

[11]Li MQ, Wang WG, Li CX, et al., 2016. Study on wear debris in water lubricated thrust bearing of nuclear main pump after rig test. Lubrication Engineering, 41(9):113-120 (in Chinese).

[12]Li W, Shi WD, Jiang XP, et al., 2012. New method for axial force balance of canned motor pump. Transactions of the Chinese Society of Agricultural Engineering, 28(7):86-90 (in Chinese).

[13]Li YC, Feng ZP, 2007. Aerodynamic design of turbine blades by using adjoint-based method and NS equation. ASME Turbo Expo: Power for Land, Sea, and Air, p.1371-1378.

[14]Liu W, Duan R, Chen C, et al., 2015. Inverse design of the thermal environment in an airliner cabin by use of the CFD-based adjoint method. Energy and Buildings, 104: 147-155.

[15]Lotz J, Naumann U, Hannemann-Taḿas R, et al., 2015. Higher-order discrete adjoint ODE solver in C++ for dynamic optimization. Procedia Computer Science, 51: 256-265.

[16]Othmer C, 2008. A continuous adjoint formulation for the computation of topological and surface sensitivities of ducted flows. International Journal for Numerical Methods in Fluids, 58(8):861-877.

[17]Othmer C, 2014. Adjoint methods for car aerodynamics. Journal of Mathematics in Industry, 4(1):6.

[18]Othmer C, de Villiers E, Weller HG, 2007. Implementation of a continuous adjoint for topology optimization of ducted flows. Proceedings of the 18th AIAA Computational Fluid Dynamics Conference, p.3947-3954.

[19]Papoutsis-Kiachagias EM, Giannakoglou KC, 2016. Continuous adjoint methods for turbulent flows, applied to shape and topology optimization: industrial applications. Archives of Computational Methods in Engineering, 23(2):255-299.

[20]Papoutsis-Kiachagias EM, Kyriacou SA, Giannakoglou KC, 2014. The continuous adjoint method for the design of hydraulic turbomachines. Computer Methods in Applied Mechanics and Engineering, 278:621-639.

[21]Poirier V, Nadarajah S, 2012. Efficient RBF mesh deformation within an adjoint-based aerodynamic optimization framework. Proceedings of the 50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, p.59.

[22]Rahim FC, Yousefi P, Aliakbari E, 2012. Simulation of the AP1000 reactor containment pressurization during loss of coolant accident. Progress in Nuclear Energy, 60:129-134.

[23]Rao ZQ, Yang CJ, 2017. Numerical prediction of effective wake field for a submarine based on a hybrid approach and an RBF interpolation. Journal of Hydrodynamics, 29(4):691-701.

[24]Rendall TCS, Allen CB, 2009. Efficient mesh motion using radial basis functions with data reduction algorithms. Journal of Computational Physics, 228(17):6231-6249.

[25]Robinson TT, Armstrong CG, Chua HS, et al., 2012. Optimizing parameterized CAD geometries using sensitivities based on adjoint functions. Computer-Aided Design and Applications, 9(3):253-268.

[26]Si ZB, Wang G, Guo YY, 2012. Analysis on thrust watts stress field of water lubrication thrust bearing. Lubrication Engineering, 37(6):57-59 (in Chinese).

[27]Su SZ, Wang PF, Xu ZB, et al., 2017. Study on maximum speed setting standard during speed up process of reactor coolant pump. Nuclear Power Engineering, 38(5):101-105.

[28]Tammisola O, Juniper MP, 2015. Adjoint sensitivity analysis of hydrodynamic stability in a gas turbine fuel injector. ASME Turbo Expo: Turbine Technical Conference and Exposition, p.1-10.

[29]Zhang JY, Zhu HW, Chun Y, et al., 2011. Multi-objective shape optimization of helico-axial multiphase pump impeller based on NSGA-II and ANN. Energy Conversion and Management, 52(1):538-546.

[30]Zhou FM, 2017. Research on the Hydraulic Design of Canned Nuclear Coolant Pump with High Efficiency, Low Axial Force and Low Hydraulic Pulsation. PhD Thesis, Dalian University of Technology, Dalian, China (in Chinese).